I do lots of web presentations to customers, so I have to keep Skype for Business turned off whenever I can to prevent the visible notifications. (We use regular Skype a lot more, which has slightly better control over this, but even there I have the notifications turned off because of the popups.)
Also, there doesn't seem to be a way to only get notified when somebody sends me a message. There is just this annoying, constant noise of people going on and offline as they go to and from meetings or customer visits, which is useless, distracting and annoying to me, and buries the useful notifications of the occasional real messages coming in.